Gravitational wave decay into dark energy

We study the decay of gravitational waves into dark energy fluctuations pi, through the processes gamma -> pi pi and gamma -> gamma pi, made possible by the spontaneous breaking of Lorentz invariance. Within the EFT of Dark Energy (or Horndeski/beyond Horndeski theories) the first process is large for the operator 1/2 (m) over tilde (2)(4) (t) delta g(00) (((3)) R + delta K-mu(nu)delta K-nu(mu) - delta K-2), so that the recent observations force (m) over tilde (4) = 0 (or equivalently alpha(H) = 0). This constraint, together with the requirement that gravitational waves travel at the speed of light, rules out all quartic and quintic GLPV theories. Additionally, we study how the same couplings affect the propagation of gravitons at loop order. The operator proportional to (m) over tilde (2)(4) generates a calculable, non-Lorentz invariant higher-derivative correction to the graviton propagation. The modi fi cation of the dispersion relation provides a bound on (m) over tilde (2)(4) comparable to the one of the decay. Conversely, operators up to cubic Horndeski do not generate sizeable higher-derivative corrections.